A process for the production of pressurized gaseous oxygen (DGOX) and small amounts of liquid oxygen (LOX) is known from publication EP 0 044 679 A1: Cold for air separation and the production of liquid product is furnished by an air refrigeration cycle. Said cycle is provided with two compressor stages in series: for compression of an air stream in the first stage to an intermediate pressure allowing work expansion of a partial stream of this air down to a lower pressure and a second compressor stage to compress the other partial stream of air to an even higher pressure allowing for throttle depressurization to the same low pressure. After the partial flows are combined and a liquid phase that is formed is branched off, the gas phase is recycled for compression, and the liquid phase is fed to the rectification after being divided into two throttled streams. In such a process, the refrigeration cycle cannot be turned off, and a returning of the refrigeration output results in energy-wasteful operation.